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In this paper, we define a new measure of the redundancy of information from a fault tolerance perspective. The partial information decomposition (PID) emerged last decade as a framework for decomposing the multi-source mutual information…

Partial information decompositions (PIDs), which quantify information interactions between three or more variables in terms of uniqueness, redundancy and synergy, are gaining traction in many application domains. However, our understanding…

The Partial Information Decomposition (PID) framework has emerged as a powerful tool for analyzing high-order interdependencies in complex network systems. However, its application to dynamic processes remains challenging due to the…

Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique…

Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…

What are the distinct ways in which a set of predictor variables can provide information about a target variable? When does a variable provide unique information, when do variables share redundant information, and when do variables combine…

A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate…

Multimodal regression aims to predict a continuous target from heterogeneous input sources and typically relies on fusion strategies such as early or late fusion. However, existing methods lack principled tools to disentangle and quantify…

Since its introduction, the partial information decomposition (PID) has emerged as a powerful, information-theoretic technique useful for studying the structure of (potentially higher-order) interactions in complex systems. Despite its…

Understanding how different information sources together transmit information is crucial in many domains. For example, understanding the neural code requires characterizing how different neurons contribute unique, redundant, or synergistic…

In many neural systems anatomical motifs are present repeatedly, but despite their structural similarity they can serve very different tasks. A prime example for such a motif is the canonical microcircuit of six-layered neo-cortex, which is…

Partial information decomposition (PID) partitions the information that a set of sources has about a target variable into synergistic, unique, and redundant contributions. This information-theoretic tool has recently attracted attention due…

Describing statistical dependencies is foundational to empirical scientific research. For uncovering intricate and possibly non-linear dependencies between a single target variable and several source variables within a system, a principled…

The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…

The partial information decomposition (PID) aims to quantify the amount of redundant information that a set of sources provides about a target. Here, we show that this goal can be formulated as a type of information bottleneck (IB) problem,…

We investigate the partial information decomposition (PID) framework as a tool for edge nomination. We consider both the $I_{\cap}^{\text{min}}$ and $I_{\cap}^{\text{PM}}$ PIDs, from arXiv:1004.2515 and arXiv:1801.09010 respectively, and we…

A reaction-coordinate--resolved information-theoretic analysis of chemical reactivity is developed using mutual information and partial information decomposition (PID). Along an intrinsic reaction coordinate (IRC), a local empirical…

We offer a new approach to the information decomposition problem in information theory: given a 'target' random variable co-distributed with multiple 'source' variables, how can we decompose the mutual information into a sum of non-negative…

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate…

Bivariate partial information decompositions (PIDs) characterize how the information in a "message" random variable is decomposed between two "constituent" random variables in terms of unique, redundant and synergistic information…